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A function f∶N→N is defined by f(x)=x^2+12. What is the type of function here?

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A function f∶N→N is defined by f(x)=x^2+12. What is the type of function here?

(a) bijective

(b) surjective

(c) injective

(d) neither surjective nor injective

The question was posed to me in class test.

My question is taken from Types of Functions topic in portion Relations and Functions of Mathematics – Class 12

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Best answer
The correct answer is (c) injective

The explanation: The above function is an injective or one-one function.

Consider f(x1)=f(x2)

∴ x1^2+12=x2^2+12

⇒x1=x2

Hence, it is an injective function.

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